from a thin piece of cardboard 40 in by 40 in, square corners are cut out so that the sidescan be folded up to make a box. What dimensions will yield a box of maximum volume

20- max volume dimension

Step-by-step explanation:

since we don't know the amount of cardboard cut off, we'll take it as "x"^^

so the bottom of the box have dimensions of 40-2x(since squares are cut from both corners in a side) by 40-2x hence we can take area of base as

(40-2x)^2

since v=base*height

lets take height as x

x(40-2x) (40-2x)=v

(40x-2x^2)(40-2x)=v

4x^3-160x^2+1600x=v

take the derivitive: 12x^2-320x+1600

factor:

4(3x^2-80x +400)=0

4(3x-20)(x-20)=0

12x-80=0

x-20=0

x=20, 6.667(reduced from 6.66666666667)

true

step-by-step explanation:

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.